Accurate travel time estimations are essential for traffic analysis and enable modern applications such as dynamic route guidance and traffic control. With the growing availability of high-resolution traffic data from GPS-enabled devices and probe vehicles, advanced models have been developed to estimate travel times more precisely. This paper proposes a sequential link estimation method for trip-level travel time estimation. The method exploits how travel times on one link are influenced by the preceding link and influence the subsequent link along a route. The method uses a chain of regression estimation models where each link's estimated travel time depends on the travel time of the adjacent link. Each estimated value is passed as input to the model for the next link, creating a chain of conditional estimates that extends from an arbitrary link to both the beginning and end of a freeway. We evaluate the proposed travel time estimation method using real-world traffic data from freeways in Sweden. The results show an average percentage error as low as 2.38 percent with a standard deviation of 1.88 percent, indicating highly accurate travel time estimates.